I recently purchased a small (370 sq ft) first-floor flat in a Victorian terraced house in central London, with a share of the freehold. The building contains four flats: the lower ground, ground, first, and a two-floor maisonette above me.

The lower ground and ground floor flats have been extended to the rear (probably many decades ago), substantially enlarging them -- around 120 sq ft of internal area, I would guess. Almost all of the neighbouring houses have had the first floor similarly extended, but for whatever reason ours has not been. Rectifying this would obviously significantly increase its rental value.

I think the issues are (1) planning permission, given that this is in a conservation area (although not listed), and, more significantly (2) coming to an arrangement with the other freeholders. The real impact on them would not be massive, as the roof area we'd be building on top of is not currently used for anything (even a roof terrace), but the window in the stairwell would be lost and perhaps a little less light would reach the lower ground's garden. On balance the second-floor maisonette could stand to benefit if we added a private roof terrace on top of the extension.

Does anyone have experience with renovating share-of-freehold flats? How have you handled/compensated the other owners?

I hope someone can help you out, I have no idea what a freehold flat is.
I'm guessing it is like a condominium or townhouse around here in the USA?
My suggestion is to ask around to the other neighbors, or folks who live in the same type of situation in your specific area. How did they do it? Around here it changes with the zoning laws from county to county and town to town.
I'm curious what you end up with, good luck.